Intrinsic relation

Intrinsic relation among measurements

The individual parts of a human body are correlated. When one part get infected, other parts also demonstrate the related symptoms. An experienced doctor will take the temperature, test the blood, ask the feeling, the appetite, and check the appearance of the part of the patient. By combining the measurements of various categories, the doctor will obtain the strongest solution which most likely leads to a correct diagnosis.

The Earth likes the body of a human being. When the shape of the Earth is changing, the relative positions among sites are also changing. Such a change can be recorded by measuring the baseline length (trilatelation), the angle between two baselines (trianguration), the relative height (leveling), the local tilt (tiltmeter), etc. On a regional scal, the "absolute" site positions are also changing. Modern space-geodesy catchs such a variation by measuring the correlated quasar pulse between two sites (baseline vector, VLBI), the carrior beat phase between satellite transmitor and the receiver (position vector, GPS), the elapse time of the laser signal (position vector, SLR), the slant distances between radar and the targets (scalar distance, SAR), etc. The change of the Earth's shape alters the gravitational field, gravimeter senses such a change. Many processes inside the Earth, such as the the earthquake rupture, fault dislocation movement, also change the shape of the Earth. These processes are reflected by the measurements of seismometer and seismicity. Through some model, such as Okada's dislocation model, these measurements can be converted to surface position variations which are comparable to the geodetic measurements. Surface mass migration also induces the undulations of the Earth's surface, such as the ocean loading and atmospheric loading. So that the measurements of tide gauge and altimeter are also convertible to surface position changes through certain Earth model and Love numbers. For large scale deformation, the whole Earth's dynamics status is perturbed, which can be detected by the dedicated measurements of polar motion and UT1. For longer period, such as the geological period, the cumulative effects of erotion, sediment, and orogenesis also change the Earth's shape significantly. By a brave assumption of that these changes are linear (or other known function of time) with time, the geological measuments can also be combined with other measurements. Because all these measurements have the intrinsic relation, i.e. all of them reflect the change of the Earth's shape, the combination of different techniques is warranted to provide stronger solution of deformation. Other benefits of the data combination are densier and wider spatial coverage and longer temporal interval, which lead to better spatial and temporal resolution of the deformation field and better accuracy (smaller formal error).

To combine the measurements of various techniques quantitatively, the change of the Earth's shape should be parameterized by common parameters. There are many choices of the parameterization, for example baseline length, baseline azimuth, network strain (or strain rate), etc. In the era of the modern space geodesy, the most commonly used parameters are the 3-d time-dependent site positions, which are also adopted by QOCA.

comming soon


	The individual parts of a human body are correlated. When one part get infected, other parts also demonstrate the related symptoms. An experienced doctor will take the temperature, test the blood, ask the feeling, the appetite, and check the appearance of the part of the patient. By combining the measurements of various categories, the doctor will obtain the strongest solution which most likely leads to a correct diagnosis.
	The Earth likes the body of a human being. When the shape of the Earth is changing, the relative positions among sites are also changing. Such a change can be recorded by measuring the baseline length (trilatelation), the angle between two baselines (trianguration), the relative height (leveling), the local tilt (tiltmeter), etc. On a regional scal, the "absolute" site positions are also changing. Modern space-geodesy catchs such a variation by measuring the correlated quasar pulse between two sites (baseline vector, VLBI), the carrior beat phase between satellite transmitor and the receiver (position vector, GPS), the elapse time of the laser signal (position vector, SLR), the slant distances between radar and the targets (scalar distance, SAR), etc. The change of the Earth's shape alters the gravitational field, gravimeter senses such a change. Many processes inside the Earth, such as the the earthquake rupture, fault dislocation movement, also change the shape of the Earth. These processes are reflected by the measurements of seismometer and seismicity. Through some model, such as Okada's dislocation model, these measurements can be converted to surface position variations which are comparable to the geodetic measurements. Surface mass migration also induces the undulations of the Earth's surface, such as the ocean loading and atmospheric loading. So that the measurements of tide gauge and altimeter are also convertible to surface position changes through certain Earth model and Love numbers. For large scale deformation, the whole Earth's dynamics status is perturbed, which can be detected by the dedicated measurements of polar motion and UT1. For longer period, such as the geological period, the cumulative effects of erotion, sediment, and orogenesis also change the Earth's shape significantly. By a brave assumption of that these changes are linear (or other known function of time) with time, the geological measuments can also be combined with other measurements. Because all these measurements have the intrinsic relation, i.e. all of them reflect the change of the Earth's shape, the combination of different techniques is warranted to provide stronger solution of deformation. Other benefits of the data combination are densier and wider spatial coverage and longer temporal interval, which lead to better spatial and temporal resolution of the deformation field and better accuracy (smaller formal error).
	To combine the measurements of various techniques quantitatively, the change of the Earth's shape should be parameterized by common parameters. There are many choices of the parameterization, for example baseline length, baseline azimuth, network strain (or strain rate), etc. In the era of the modern space geodesy, the most commonly used parameters are the 3-d time-dependent site positions, which are also adopted by QOCA.
	comming soon